Nuprl Lemma : free-vs-inc_wf
∀[S:Type]. ∀[K:RngSig]. ∀[s:S]. (<s> ∈ Point(free-vs(K;S)))
Proof
Definitions occuring in Statement :
free-vs-inc: <s>,
free-vs: free-vs(K;S),
vs-point: Point(vs),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
basic-formal-sum: basic-formal-sum(K;S),
all: ∀x:A. B[x],
free-vs-inc: <s>,
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
formal-sum: formal-sum(K;S),
btrue: tt,
bfalse: ff,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
top: Top,
mk-vs: mk-vs,
vs-point: Point(vs),
free-vs: free-vs(K;S)
Lemmas referenced :
rng_sig_wf,
bag_wf,
rng_one_wf,
rng_car_wf,
single-bag_wf,
bfs-equiv-rel,
bfs-equiv_wf,
basic-formal-sum_wf,
subtype_quotient,
rec_select_update_lemma
Rules used in proof :
universeEquality,
extract_by_obid,
because_Cache,
thin,
isectElimination,
isect_memberEquality,
hypothesisEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalRule,
sqequalHypSubstitution,
hypothesis,
applyEquality,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
lambdaEquality,
independent_pairEquality,
cumulativity,
productEquality,
dependent_functionElimination,
independent_isectElimination,
voidEquality,
voidElimination
Latex:
\mforall{}[S:Type]. \mforall{}[K:RngSig]. \mforall{}[s:S]. (<s> \mmember{} Point(free-vs(K;S)))
Date html generated:
2018_05_22-PM-09_46_16
Last ObjectModification:
2018_01_09-PM-00_26_39
Theory : linear!algebra
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